I have some question about math. I don't understand about it. Can you help me?

1. How many bit strings of length 10 that neither start nor end with 007?
2. How many functions are there from the set {1, 2, 3, 4, 5} to the set {0, 1}?
3. Show that if 7 integers are selected from {1,2,...,10},there must be at least 2 pairs of these integers with the sum 11(for example 5 6=11)?
4. How many permutations of the letters ABCDEFGH contain the string BA?
5. Place these permutations of{1,2,3,4,5,6}in lexicographic order:234561,231456,165432,156423,543216?
6. Which is more likely: rolling a total of 8 when two dice are rolled or rolling a total of 8 when three dice are rolled?
7. Let R be the relation R = {(a, b)|a <b}on the set of integers. Find R−1 and R?
8. Which projection mapping is used to delete the second and the fourth components of a 6-tuple?
9. Let R be the relation on the set{1,2,3,4,5}containing the ordered pairs(1,2),(2,5),(3,4),(3,1),(4,2),(5,1),(5,3),and (5,4).Find R2?